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arXiv · 2604.00663

Invariant idempotent $\ast$-measures for generalized iterated function systems

Natalia Mazurenko·Mykhailo Zarichnyi
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Abstract

The notion of $\ast$-measure on a compact Hausdorff space can be defined for arbitrary continuous triangular norm $\ast$. The well-known Hutchinson-Barnsley theory deals with the iterated function systems (IFSs) of probability measures and establishes existence and uniqueness of invariant measures. In the previous paper, IFSs of $\ast$-measures were considered. In the present paper we deal with generalized invariant function systems (GIFSs) of $\ast$-measures, which are counterparts of GIFSs in the sense of Mihail and Miculescu. The notion of invariant $\ast$-measure is introduced for such GIFSs and we prove existence and uniqueness of such elements.

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BibTeXRIS

Natalia Mazurenko, Mykhailo Zarichnyi. 2026-04-01. Invariant idempotent $\ast$-measures for generalized iterated function systems. https://arxiv.org/abs/2604.00663

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